WASHINGTON, March 12 (Reuters) - U.S. President Barack Obama will not accept action by Congress that “locks in” spending caps enacted in 2011, White House budget director Shaun Donovan said on Thursday as Republicans hashed out final details on their own budget plans.

Lawmakers from both parties have said they want to ease the “sequester” spending constraints, but Republican budget proposals to be unveiled next week are largely expected to adhere to them, keeping military and domestic discretionary spending at 2006 levels, about $1.016 trillion.

“The president has been very clear. He will not accept a budget that locks in the sequester going forward and he will not accept a budget that severs the vital link between defense and non-defense,” Donovan told a news conference at the Capitol.

The automatic, across-the-board cuts that sprang from a 2011 budget deal and run through 2021 spread the pain equally between military and domestic programs and barred Congress from diverting funds to one side from the other.

Republican senators worried about the cuts eroding military readiness said on Thursday they were nearing agreement to allow the caps to nominally stay in place for the non-binding budget document while they launched a separate process to look for savings to increase some spending.

Senator Lindsey Graham, a pro-military Republican from South Carolina who is weighing a run for president in 2016, said he would be willing to close some tax breaks for the wealthy if Democrats were willing to offer savings on federal benefits. The hunt for savings can start through a deficit-neutral military reserve fund in the budget, he said.

“At the end of the day if there’s not a pathway forward to fix sequestration on the defense side, I won’t vote for a budget,” Graham told reporters.

Donovan said Congress should follow a model set by Senator Patty Murray and Representative Paul Ryan in a 2013 budget deal that eased the sequester caps over the past two years. Obama’s budget in January proposed lifting military and domestic spending by $74 billion above the caps in fiscal 2016.

Although the president doesn’t sign the budget resolution from Congress, he does have the ability to veto spending legislation. Asked if Obama would veto spending bills that conform to the across-the-board spending caps for fiscal 2016, Donovan stopped short, saying those would be reviewed as they are written later this year. (Reporting by David Lawder; Editing by Eric Beech)